VI. Suppose 5 of the population have a certain disease. A laborator.pdf

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VI. Suppose 5% of the population have a certain disease. A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease. a. What is the probability of testing positive? b. What is the probability that a randomly selected person does not has the disease given that this person is testing positive? Solution PROBABILITY OF GETTING DISEASE ,P(A)=0.05 PROBABILITY OF NOT GETTING DISEASE,P(B)=(1-0.05)=0.95 LET E BE EVENT OF OCCURING POSITIVE READING PROBABILITY OF GETTING POSITIVE READING who have the disease ,P(E/A)=0.95 PROBABILITY OF GETTING POSITIVE READING who DO NOT have the disease,P(E/B)=0.10 A)the probability of testing positive,P(E) B)the probability that a randomly selected person does not has the disease given that this person is testing positive,P(B/E) FROM BAYES THEOREM P(B/E)=P(B)*P(E/B)/[P(B)*P(E/B)+P(A)*P(E/A)] =[0.95*0.10]/[(0.95*0.10)+(0.05*0.95)] =[0.095]/[0.095+0.0475] =0.667 HENCE,P(B/E)=0.67.

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B)the probability that a randomly selected person does not has the disease given that this person
is testing positive,P(B/E)
FROM BAYES THEOREM
P(B/E)=P(B)*P(E/B)/[P(B)*P(E/B)+P(A)*P(E/A)]
=[0.95*0.10]/[(0.95*0.10)+(0.05*0.95)]
=[0.095]/[0.095+0.0475]
=0.667
HENCE,P(B/E)=0.67

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The usefulness of diagnostic tests, that is their ability to detect a person with disease or exclude a person without disease, is usually described by terms such as sensitivity, specificity, positive predictive value and negative predictive value (NPV). Many clinicians are frequently unclear about the practical application of these terms (1). The traditional method for teaching these concepts is based on the 2 × 2 table (Table 1). A 2 × 2 table shows results after both a diagnostic test and a definitive test (gold standard) have been performed on a pre-determined population consisting of people with the disease and those without the disease. The definitions of sensitivity, specificity, positive predictive value and NPV as expressed by letters are provided in Table 1. While 2 × 2 tables allow the calculations of sensitivity, specificity and predictive values, many clinicians find it too abstract and it is difficult to apply what it tries to teach into clinical practice as patients do not present as ‘having disease’ and ‘not having disease’. The use of the 2 × 2 table to teach these concepts also frequently creates the erroneous impression that the positive and NPVs calculated from such tables could be generalized to other populations without regard being paid to different disease prevalence. New ways of teaching these concepts have therefore been suggested.

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